<p>This paper studies a single-phase nine-level rectifier with coupled inductance. Aiming at the problems of slow response speed and poor anti-interference when the traditional PI controller is used in the voltage outer loop and the chattering problems when the traditional sliding mode control is used, an improved fractional-order terminal sliding mode control strategy (FOTSMC) is proposed. First, the principle of the nine-level generation of the rectifier is analyzed, and the required mathematical model is established. Second, the outer loop fractional-order terminal sliding mode control algorithm is designed for the rectifier, and the system stability is proved. Finally, the simulation and experimental results show that the proposed improved fractional-order terminal sliding mode control strategy has the advantages of faster convergence speed, no startup overshoot, better dynamic performance, and minor system chattering, which verifies the effectiveness and correctness of the proposed algorithm.</p>